Hertzian Testing to Obtain Flaw Distributions in High Strength Glasses and Glass-Ceramics

作者：Reimanis Ivar E^*; Schaut Robert A

来源：Journal of the American Ceramic Society, 2016, 99(11): 3712-3718.

DOI：10.1111/jace.14407

• hertzian
• flaw distribution
• glass
• glass-ceramics
• fracture
• strength

Hertzian testing is applied to obtain flaw distributions in two fusion-drawn glasses and two glass-ceramics. A tungsten carbide sphere (diameter either 1.0, 2.5, or 5.0 mm) was used to produce surface cracks (ring cracks and cone cracks). Two theoretical approaches were employed to describe the data. Both approaches are only descriptive for very high strength materials in which the surface flaw sizes are small (e.g., <1 m). In the first, a Weibull distribution for strength was assumed, and an expression for the probability of fracture was derived based on the stress field around the indent contact area. The unique aspect of this is that the stress field used includes material that has been probed at loads below the fracture load. A Weibull plot with this expression shows a slope of m + 2, where m is the conventional Weibull modulus. For the four different materials, the Weibull modulus varied between 8.0 for -quartz glass-ceramic to 14.2 for fusion drawn alumni silicate glass. The second theoretical approach employs a modification of the method of Poloniecki and Wilshaw (the PW Method) to describe the distributions of very small flaws. The modification removes the need to bin the flaw distribution data. The modified PW Method revealed distinct differences in the flaw distributions between the four materials. These differences are consistent with the different Weibull moduli determined by ranking the different materials according to flaw size. However, Hertzian testing only probes relatively small flaw sizes and thus may differ from typical tensile or bending tests; nevertheless, the method should be applicable for extremely high strength materials.

• 出版日期2016-11